HI Denise....
Most of us use origin to cut unless we need fold or score lines (or writing) and need the placement to hold - so let me start there.
Will try a simple example as I don't want to get too wordy on this one. Let's say you have a 4" square and it's in the middle of your 12" mat.
If you are cutting with origin and you set it on the lower (front) right hand corner of your paper, when you hit cut, the bottom right corner of the square will be at your origin point and the square will cut in that center.
If you are cutting with WYSIWYG, when you set the origin, that is telling the machine where the corner of your material is, and the square will then cut in the middle of your 12x12" piece of paper if that is what you have. It cuts where you have it on the mat.
Two things - use the test pen instead of a blade and draw the shapes - that's what it's there for and it will help you make sense of it and not ruin blades in the process.
Also, when you go to cut you will have a preview window on the right side of the pop up window which will show you exactly where your shape is going to cut and that may help catch any issues too - it's great when I remember to look there first!
Hope that helps.